Applications of Wavelet Transform and Artificial Neural Network in Digital Signal Detection for

Indoor Optical Wireless Communication

Sujan Rajbhandari

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Sujan Rajbhandari

Supervisors

Prof . Maia AngelovaProf. Z. Ghassemlooy

Prof. Jean-Pierre Gazeau

Optical Wireless Communication

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Light as the carrier of information

Also popularly known as free space optics (FSO) or Free Space Photonics (FSP) or open-air photonics .

Indoor or outdoor

Transmission Format

Transmitted signal ‘1’ presence of an optical pulse ‘0’ absence of an optical pulse

Sujan Rajbhandari

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Transmitted OOK

Normalized Time

Am

pitu

de

0 1 1 0 0 0 11 0 1

Links

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Non-LOS

Multipath Propagation Intersymbol interference (ISI) Difficult to achieve high data

rate if ISI is not mitigated.

Non-LOS

Multipath Propagation Intersymbol interference (ISI) Difficult to achieve high data

rate if ISI is not mitigated.

RxRxTxTx

LOSLOS

No multipath propagation Noise and device speed

are limiting factors Possibility of blocking

TxTx

RxRx

Received Signal

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Non-LOSNon-LOS

0 2 4 6 8 10-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Normalized Time

Am

plit

ud

e

Received signal for non-LO OOK

LOSLOS

0 2 4 6 8 10

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Received OOK for LOS links

Normalized Time

Am

plit

ud

e

Classical Digital Signal Detection

Set a threshold level.

Compared the received signal with the threshold level

Set ‘1’ if received signal is greater than threshold level

Set ‘0’ is received signal is less than threshold level.

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Classical signal detection techniques: Assumptions

The statistical of noise is known.

Maximise the signal to noise ratio for unknown noise with known statistics.

Channel characteristics are known( at least partially ) and generally assume to be linear.

Digital signal Reception:Problem of feature extraction and pattern

classification

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Received signal ‘1’ signal + interference ‘0’ interference only (noise and intersymbol

interference (ISI)) .

Interference only signal + interference

0 0.2 0.4 0.6 0.8 1-0.5

0

0.5

1

1.5

2

2.5

Normalized Time

Am

plit

ud

e

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

1.5

Normalized Time

Am

plit

ud

e

Sujan Rajbhandari

Receiver from the Viewpoint of Statistics9

Testing a Null Hypothesis of

a) Received signal is interference only

against

b) Alternative Hypothesis of received signal is signal

plus interference

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Problem of Feature Extraction and Pattern Classification

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Receiver Block diagram

OpticalReceiver

Wavelet Transform

Artificial Neural Network

Threshold Detector

Feature ExtractionFeature

ExtractionPattern

ClassificationPattern

Classification

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Time- Frequency analysis

Fourier Transform

Time-frequency mapping

What frequencies are present in a signal but fails to give picture of where those frequencies occur.

No time resolution.

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Time- Frequency analysis

Windowed Fourier Transform (Short time Fourier

transform)

Chop signal into equal sections

Find Fourier transform of each section

Disadvantages

Problem how to cut a signal

Fixed time and frequency resolution

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Time- Frequency analysis

Continuous Wavelet Transform (CWT) Vary the window size to vary resolution

(Scaling). Large window for precise low-frequency information,

and shorter window high-frequency information Based on Mother wavelet. Mother Wavelet are well localised in time.(Sinusoidal

wave which are the based of Fourier transform extend from minus infinity to plus infinity)

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Continues Wavelet Transform

Where are wavelets and s and τ are scale and

translation. Translation time resolution scale frequency resolution Wavelets are generated from scaling and translation

the Mother wavelet.

dtttfs s )(*)(),( ,

)(1

)( ,, s

t

st ss

dsdtstf s )(),()( ,

CWT of Signal f(t) and reconstruction is given by

)(, ts

Discrete Wavelet Transform

• Dyadic scales and positions• DWT coefficient can efficiently be obtained by filtering and down sampling1

1 Mallat, S. (1989), "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, pp. 674-69

Artificial Neural Network

Fundamental unit : a neuron

Based on biological neuron

Capability to learn

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).(1

n

kkk wxbfy

b

wn y

x1

f(.)∑

w1

Output

xn

.

.

.

Artificial Neural Network

Input layer , hidden layer(s) and

output layer

Extensively used as a classifier

Supervised and unsupervised

learning.

Weight are adjust by

comparing actual output and

target output

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Input Layer

Hidden Layer 1

Hidden Layer 2

Output

Input Layer

Hidden Layer 1

Hidden Layer 2

Output

Feature Extraction:Discrete Wavelet Transform

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DWT of Interference onlyDWT of Interference only DWT of signal +InterferenceDWT of signal +Interference

0 2 4 6 8 10 12 14 16 18 20-1

0

1

a 3

0 2 4 6 8 10 12 14 16 18 20-1

0

1

d3

0 5 10 15 20 25 30 35 40-1

0

1

d2

0 10 20 30 40 50 60 70 80-1

0

1

d1

0 2 4 6 8 10 12 14 16 18 200

1

2

a 3

0 2 4 6 8 10 12 14 16 18 20-0.5

0

0.5

d3

0 5 10 15 20 25 30 35 40-0.5

0

0.5

d2

0 10 20 30 40 50 60 70 80-0.5

0

0.5

d1

• Significant difference in approximation coefficient ,a3.• No difference in other details coefficients. (Details coefficient are due to the high frequency component of signal , mainly due to noise.)

• Significant difference in approximation coefficient ,a3.• No difference in other details coefficients. (Details coefficient are due to the high frequency component of signal , mainly due to noise.)

Denoising

The high frequency component can be removed or suppressed.

Two Approach Taken

1. Threshold approach in which the detail coefficients are suppressed by either ‘hard’ or ‘soft’ thresholding.

2. Coefficient removal approach in which detail coefficients are completely removed by making it zero.

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De-noised Signal

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LOS LinksLOS Links

0 2 4 6 8 10-0.5

0

0.5

1

1.5

Normalized Time

Am

plit

ud

e

Denoised signal for LOS links

Received signal

Denoised Signal(Threshold approach)

Denoised SignalCoeff. Removal Approach

Non-LOS LinksNon-LOS Links

0 2 4 6 8 10-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Normalized TimeA

mp

litu

de

Denoised signal for non-LOS links

Denoising (Threshold Approach)

Denoised Signal(Coeff. Removal Approach)

Received Signal

•Denoising effectively removes high frequency component.•Equalization is necessary for non-LOS links•Identical performance for both de-noising approaches.

21Artificial Neural Network : Pattern Classifier

Artificial Neural Network can be trained to differentiate the interference from signal plus interference.

DWT are fed to ANN. ANN is first trained to classify by providing

examples. ANN can be utilized both as a pattern

classifier and equalizer.

Results

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The Coefficient removal approach (CRA) of denoising gives the best result. Easier to train ANN using CRA as the DWT coefficients are removed by 8 folds if 3 level of DWT is taken. Effective for detection and equalization.

Figure: The Performance of On-off Keying at 150Mbps for diffused channel with a Drms of 10ns

Comparison with traditional methods

•Maximum performance of 8.6dBcompared to linear equalizer• performance depends on the mother wavelets.• Discrete Meyer gives the best performance and Haar the worst performance among studied mother wavelet

Conclusion

Digital signal detection can be reformulated as feature extraction and pattern classification.

Discrete wavelet transform is used for feature extraction.

Artificial Neural Network is trained for pattern classification.

Performance can further be enhance by denoising the signal before classifying it.

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Thank You

Discussions